Open Access
2018 S-Limited Shifts
Benjamin Matson, Elizabeth Sattler
Real Anal. Exchange 43(2): 393-416 (2018). DOI: 10.14321/realanalexch.43.2.0393


In this paper, we explore the construction and dynamical properties of \(\mathcal{S}\)-limited shifts. An \(S\)-limited shift is a subshift defined on a finite alphabet \(\mathcal{A} = \{1, \ldots,p\}\) by a set \(\mathcal{S} = \{S_1, \ldots, S_p\}\), where \(S_i \subseteq \mathbb{N}\) describes the allowable lengths of blocks in which the corresponding letter may appear. We give conditions for which an \(\mathcal{S}\)-limited shift is a subshift of finite type or sofic. We give an exact formula for finding the entropy of such a shift and show that an \(\mathcal{S}\)-limited shift and its factors must be intrinsically ergodic. Finally, we give some conditions for which two such shifts can be conjugate, and additional information about conjugate \(\mathcal{S}\)-limited shifts.


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Benjamin Matson. Elizabeth Sattler. "S-Limited Shifts." Real Anal. Exchange 43 (2) 393 - 416, 2018.


Published: 2018
First available in Project Euclid: 27 June 2018

zbMATH: 06924897
MathSciNet: MR3942586
Digital Object Identifier: 10.14321/realanalexch.43.2.0393

Primary: 37B10

Keywords: Entropy , S-gap shift , shift space

Rights: Copyright © 2018 Michigan State University Press

Vol.43 • No. 2 • 2018
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